In general, data visualization transforms numeric or textual information into a graphical display format to assist users in understanding underlying trends and principles in the data. Effective data visualization complements and, in some instances, supplants numbers and text as a more intuitive visual presentation format than raw numbers or text alone. However, graphical data visualization is constrained by the physical limits of computer display systems. Two-dimensional and three-dimensional visualized information can be readily displayed. However, visualized information in excess of three dimensions must be artificially compressed if displayed on conventional display devices. Careful use of color, shape and temporal attributes can simulate multiple dimensions, but comprehension and usability become difficult as additional layers of modeling are artificially grafted into a two- or three-dimensional display space.
Mapping multi-dimensional information into a two- or three-dimensional display space potentially presents several problems. For instance, a viewer could misinterpret dependent relationships between discrete objects displayed adjacently in a two or three dimensional display. Similarly, a viewer could erroneously interpret dependent variables as independent and independent variables as dependent. This type of problem occurs, for example, when visualizing clustered data, which presents discrete groupings of related data. Other factors further complicate the interpretation and perception of visualized data, based on the Gestalt principles of proximity, similarity, closed region, connectedness, good continuation, and closure, such as described in R. E. Horn, “Visual Language: Global Communication for the 21st Century,” Ch. 3, MacroVU Press (1998), the disclosure of which is incorporated by reference.
Conventionally, objects, such as clusters, modeled in multi-dimensional concept space are generally displayed in two- or three-dimensional display space as geometric objects. Independent variables are modeled through object attributes, such as radius, volume, angle, distance and so forth. Dependent variables are modeled within the two or three dimensions. However, poor cluster placement within the two or three dimensions can mislead a viewer into misinterpreting dependent relationships between discrete objects.
Consider, for example, a group of clusters, which each contain a group of points corresponding to objects sharing a common set of traits. Each cluster is located at some distance from a common origin along a vector measured at a fixed angle from a common axis. The radius of each cluster reflects the number of objects contained. Clusters located along the same vector are similar in traits to those clusters located on vectors separated by a small cosine rotation. However, the radius and distance of each cluster from the common origin are independent variables relative to other clusters. When displayed in two dimensions, the overlaying or overlapping of clusters could mislead the viewer into perceiving data dependencies between the clusters where no such data dependencies exist.
Conversely, multi-dimensional information can be advantageously mapped into a two- or three-dimensional display space to assist with comprehension based on spatial appearances. Consider, as a further example, a group of clusters, which again each contain a group of points corresponding to objects sharing a common set of traits and in which one or more “popular” concepts or traits frequently appear in some of the clusters. Since the distance of each cluster from the common origin is an independent variable relative to other clusters, those clusters that contain popular concepts or traits may be placed in widely separated regions of the display space and could similarly mislead the viewer into perceiving no data dependencies between the clusters where such data dependencies exist.
The placement of cluster groups within a two-dimensional display space, such as under a Cartesian coordinate system, also imposes limitations on semantic interrelatedness, density and user interface navigation. Within the display space, cluster groups can be formed into “spines” of semantically-related clusters, which can be placed within the display space with semantically-related groups of cluster spines appearing proximally close to each other and semantically-unrelated cluster spine groups appearing in more distant regions. This form of cluster spine group placement, however, can be potentially misleading. For instance, larger cluster spine groups may need to be placed to accommodate the placement of smaller cluster spine groups while sacrificing the displaying of the semantic interrelatedness of the larger cluster spine groups. Moreover, the density of the overall display space is limited pragmatically and the placement of too many cluster spine groups can overload the user. Finally, navigation within such a display space can be unintuitive and cumbersome, as large cluster spine group placement is driven by available display space and the provisioning of descriptive labels necessarily overlays or intersects placed cluster spine groups.
One approach to depicting thematic relationships between individual clusters applies a force-directed or “spring” algorithm. Clusters are treated as bodies in a virtual physical system. Each body has physics-based forces acting on or between them, such as magnetic repulsion or gravitational attraction. The forces on each body are computed in discrete time steps and the positions of the bodies are updated. However, the methodology exhibits a computational complexity of order O(n2) per discrete time step and scales poorly to cluster formations having a few hundred nodes. Moreover, large groupings of clusters tend to pack densely within the display space, thereby losing any meaning assigned to the proximity of related clusters.
Therefore, there is a need for an approach to providing a visual display space reflecting tighter semantic interrelatedness of cluster spine groups with increased display density. Preferably, such an approach would further form the cluster spine groups by semantically relating entire cluster spines, rather than individual anchor points within each cluster spine.
There is a further need for an approach to orienting semantically-related cluster spine groups within a two-dimensional visual display space relative to a common point of reference, such as a circle. Preferably, such an approach would facilitate improved user interface features through increased cluster spine group density and cluster spine group placement allowing improved descriptive labeling.